An approach to Elliptic Curve Cryptography with AOP oriented to Hardware

• Luckas A. Farias
• Bruno C. Albertini
• Paulo S. L. M. Barreto

Resumo

This work describes a family of binary Edwards curves that admits modular reductions (an operation that can be responsible for up to 30% of the processing time in point arithmetic) twice as fast than the best usual settings, while essentially being as secure as a binary elliptic curve can be (in terms of being rigid and twist-safe). Moreover, we present a hardware architecture with a generic VHDL description that can be synthesized to any FPGA with enough area to support the circuit. For this architecture, we are able to execute a point multiplication by scalar on F562 in 2.28ms on Cyclone 4 GX, in 1.23ms on Virtex7 and in 1.01ms on Zynq7020.